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completely wrong! One just doesn't do that in this part of the world. Here
one gives birthday children questions, not answers! So therefore I thought
to myself, okay, I'll present my answers at some other opportunity; today,
on the occasion of this birthday celebration, I too will come with two ques-
tions. And it's not just about questions but rather—we are, indeed, here in
the Center for Interdisciplinary Research—about two research programs
into still unsolved problems of the social sciences. I thought I'd present
these problems today, for I have the feeling that if one would concern
oneself with these questions one could make an essential contribution to
social theory.
What are these two questions about? The first problem or research
program has to do with an extension, or perhaps I should say: with a deep-
ening, of recursive functions. You all know about the unprecedented suc-
cesses of the recursive functions that are in constant use in chaos theory
and indeed elsewhere. But I have the feeling that these results of chaos
research can be applied by sociology only metaphorically. Why? All chaos
research is concerned with functions, and functions are only relations
between numbers, at best, complex numbers. A function can be quadratic,
one gives this function a two, out comes a four, and one gives this function
a three, and out comes a nine. It operates only on numbers, but sociology
doesn't work with numbers: sociology is interested in functions. And func-
tions of functions one calls functors. A functor is, so to speak a system that
is intended to coordinate one group of functions with another group, and
so today I propose to develop a research program in which one is concerned
with recursive functors. So that's problem number one.
Problem number two that I'd like to present today is a theory of com-
positions. It consists in developing a system of composition, and, indeed, a
system of composition for systems. What is this problem about? I have
System
A
, I have a System
B
, and now I'd like to integrate both of these
into a System
C
. What do the rules consist of that allow a new System
C
to
arise, the rules of integration, of composition? Is it a kind of addition, a kind
of integration? We've got all the best words for it, but what does the for-
malism for such problems look like? Today one could also provide the com-
position problem with another name: It's about, for example, the problem
of the Croats, the Bosnians, the Herzegovinians—one could call it the
Vance-Owen Problem. These are the problems that we confront in social
theory today. How can one solve this problem? Or in a different sense it is
also about the problem of autopoiesis: how can I bring an autopoietic
System
A
into a relationship with another autopoietic System
B
in such a
way that a new System
C
arises, itself an autopoietic system? Unfortunately,
the poets or autopoets who invented autopoiesis have given us no rules for
the compositional possibilities of such autopoietic systems. They have, to be
sure, applied indices, but that isn't really a fundamental theory of compo-
sition. These are, in brief, my two problems.
Now of course you'll say, “for heaven's sakes, we're sociologists, and here
Heinz von Foerster comes with fundamental mathematical problems—what
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